A protest in Quetta after the killing of Osama Bin Laden Photograph: Banaras Khan/AFP/Getty Images

The Obama administration is demanding an explanation from Pakistan on how Osama bin Laden was able to hide in the country for so long before he was killed by US special forces.

Bin Laden was staying in a prominent million-dollar, high-security residence in an area full of soldiers and close to the country's premier military academy.

John Brennan, a counter-terrorism adviser to Barack Obama, told journalists at the White House: "People have been referring to this as hiding in plain sight. We are looking at how he was able to hide out there for so long."

He added it was "inconceivable" that Bin Laden did not enjoy a "support system" in Pakistan.

The al-Qaida leader was killed by US special forces who attacked the compound in Abbottabad, about 30 miles from Islamabad, on Sunday, according to US officials. His body was taken by helicopter to a US aircraft carrier in the Arabian Gulf and buried at sea.

One of his adult sons was also killed, as was a woman, who the White House claimed had been used by Bin Laden as a shield in the attack.

Obama said: "The world is safer. It is a better place because of the death of Osama bin Laden."

Although Obama, Hillary Clinton, the secretary of state, and Brennan expressed the importance of Pakistan in helping to fight al-Qaida, the presence of Bin Laden so close to the capital and just streets away from the principal training ground for the country's officer corps threatened to create a fresh rift in US-Pakistan relations.

Such was the American distrust of the notoriously leaky Pakistan government that it did not even inform it of the raid in its own territory until after US helicopters had cleared Pakistani airspace.

Members of Congress threatened to withhold economic aid to Pakistan over the affair. Carl Levin, a Democrat who heads the powerful Senate armed services committee, reflected scepticism in the US about Bin Laden's ability to remain hidden in Pakistan. "I think the Pakistani army and intelligence have a lot of questions to answer given the location, the length of time and the apparent fact that this facility was actually built for Bin Laden and its closeness to the central location of the Pakistani army," he told a press conference. The US will step up pressure on Pakistan to hand over the Taliban leader, Mullah Omar and Bin Laden's deputy, Ayman al-Zawahiri, if they are in Pakistan. The death of Bin Laden could also lead to a rethink of the scale of the US involvement in Afghanistan.

Embassies, airports and defence bases were placed on high alert for possible retaliation by al-Qaida sympathisers. David Cameron warned of a continuing threat from "extremist terrorism" but hailed a "massive step forward".

The mood in the US was one of celebration as Americans gathered at Ground Zero in New York, pleased finally to have retribution. Obama called it "a good day for America" that had made the world a safer place. Obama will visit Ground Zero on Thursday to meet the families of those killed in the September 11 attacks.

The White House and Pentagon provided fresh details of the mission by Navy Seals. Bin Laden was killed with a shot to the head, according to US officials, and was also shot once in the chest. CNN last night reported "administration officials" as saying Bin Laden did not take up or fire a weapon when the US special forces landed. One of the troops shouted soon afterwards "Geronimo EKIA" – geronimo enemy killed in action – the station reported.

Brennan denied that the special forces had been told not to capture him, only kill him. "If we had the opportunity to take him alive, we would have done," he said.

Clinton, anxious not to alienate a partner that may yet be needed for actions against al-Qaida and the Taliban, emphasised America's "close co-operation" with Pakistan. She said: "In fact, co-operation with Pakistan helped lead us to Bin Laden and the compound in which he was hiding."

The Pakistan government welcomed the killing as "a major setback to terrorist organisations around the world".

But the former Pakistan president Pervez Musharraf reflected his country's unease over a breach of sovereignty. "America coming to our territory and taking action is a violation of our sovereignty," Musharraf told CNN.

"Handling and execution of the operation [by US forces] is not correct. The Pakistani government should have been kept in the loop."

Clinton suggested that US policy on Afghanistan would not shift, but other officials hinted the dynamics may have changed. The Pentagon only wants to see a token force of a few thousand withdrawn beginning in the summer, but Obama may want a more significant reduction.

An Afghan government official said he feared the death would give "justification for US premature disengagement from the region". It was a view echoed by Ahmed Wali Massoud, an Afghan politician and brother of Ahmed Shah Massoud, the legendary resistance fighter who was assassinated just two days before the September 11 attacks on the orders of Bin Laden.

"Obviously this is a huge relief for our family that justice has been done, but it also raises other concerns," Massoud said. "Already the US has been thinking about shifting its policy on the war on terror and there is a risk that the American public will continue to question why their troops are still fighting there," he said.

One of the most senior American officers serving in Afghanistan, General William Caldwell, told the Guardian the death might encourage moderate elements within the Taliban to give up.

John Taylor whose daughter Carrie, 24, was killed in the 7/7 bombings, said he would be celebrating. He said: "This is poetic justice for my daughter. This is a little piece of justice for Carrie and the thousands around the world who have been killed as a result of his actions."